analogous
发表于 2025-3-23 12:51:09
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外观
发表于 2025-3-23 16:14:28
https://doi.org/10.1007/3-540-06721-3A BA . is said to satisfy the κ-. (κ-cc) if every disjoint subset of . has power <κ. Thus for κ non-limit, this is the same as saying that the cellularity of . is <κ. Of most interest is the ω.-chain condition, called ccc for short (countable chain condition). We shall return to it below.
衰老
发表于 2025-3-23 20:37:28
https://doi.org/10.1007/3-540-06721-3Recall that Depth(.) is the supremum of cardinalities of subsets of . which are well ordered by the Boolean ordering. There are two main references for results about this notion: McKenzie, Monk and (implicitly) Grätzer, Lakser .
Intellectual
发表于 2025-3-24 00:14:14
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GIBE
发表于 2025-3-24 03:45:09
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网络添麻烦
发表于 2025-3-24 06:31:57
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locus-ceruleus
发表于 2025-3-24 12:09:09
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Adornment
发表于 2025-3-24 15:00:38
https://doi.org/10.1007/3-540-06721-3We denote .. The behaviour of this function under algebraic operations is for the most part obvious. Note, though, that questions about its behaviour under ultraproducts are the same as the well-known and difficult problems concerning the cardinality of ultraproducts in general.
aesthetic
发表于 2025-3-24 20:29:29
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Deject
发表于 2025-3-24 23:19:23
https://doi.org/10.1007/3-540-06721-3First of all, note that if F is a non-principal ultrafilter on a BA ., then.. To see this, suppose that X is a finite set of non-zero elements of . which is dense in ..